In this paper, we propose a new matrix completion based MIMO radar (MIMO-MC) using a random unitary matrix as the waveform matrix. We show that the corresponding data matrix has a good incoherent property, which guarantees accurate reconstruction of the data matrix from partial entries. The derived performance guarantees hold for any random unitary waveforms and radar precoder. This indicates that the proposed MIMO-MC approach can dynamically adapt its waveform/precoding for the purpose of waveform security or interference suppression in low SINR conditions, without affecting the performance of data matrix completion. We further investigate the application of MIMO-MC transmit precoding for clutter mitigation and spectrum sharing with wireless communications.